2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222292Bonahon conjectured that compact convex cores with totally geodesic boundary uniquely minimize volume over all hyperbolic 3-manifolds in the same homotopy class. This paper proves Bonahon's conjecture. The proofs extend the techniques of Besson-Courtois-Gallot.33 pagesGeometric Topology53C25; 57N10text